The Robert Smyth School
Mathematics Faculty
Topic 6
Ratio HW 2
Innovation & excellence
Topic 6 (foundation) – Homework on Using Ratios
1.
The frequency diagram shows the distribution of shoe sizes for a class of 40 pupils.
10
8
Boys
Girls
6
Frequency
4
2
0
(a)
2
3
4
5
Shoe size
6
7
What is the ratio of girls to boys in the class?
Give your answer in its simplest form.
..................................................................................................................................
..................................................................................................................................
Answer ....................................
(b)
(2)
What percentage of the class have shoe size 6?
..................................................................................................................................
..................................................................................................................................
Answer ...................................... %
2.
(3)
A packet contains 12 fibre-tipped pens.
Henry and Alice share them in the ratio 1 : 3
How many does Alice receive?
................................…………………………………………………………………………
................................…………………………………………………………………………
................................…………………………………………………………………………
Answer ................................................
(2)
The Robert Smyth School
1
The Robert Smyth School
Mathematics Faculty
Topic 6
Ratio HW 2
Innovation & excellence
3.
Craig and Sophie share 40 chocolates.
They divide them in the ratio 1 : 4 with Sophie having the larger share.
How many chocolates does Sophie have?
...............................................................................................................................................
...............................................................................................................................................
Answer .......................................................................
(Total 2 marks)
4.
Two singers receive £80 between them.
They divide their pay in the ratio of the number of songs they each sing.
Dan sings one song and Angela sings four songs.
How much does Dan receive?
................................…………………………………………………………………………
................................…………………………………………………………………………
Answer £ ................……………………………
(2)
5.
The total number of marks for a test is 40.
(a)
The marks are divided between Section A and Section B in the ratio 4 : 1
(i)
How many marks are there for Section B?
...........................................................................................................................
...........................................................................................................................
Answer ..........................................................................
(2)
(ii)
How many more marks are there for Section A than for Section B?
...........................................................................................................................
Answer ..........................................................................
(1)
(b)
Shahid gains 24 marks out of 40 in the test.
Work out his mark as a percentage.
.....................................................................................................................................
Answer .......................................................................... %
(2)
(Total 5 marks)
The Robert Smyth School
2
The Robert Smyth School
Mathematics Faculty
Topic 6
Ratio HW 2
Innovation & excellence
6.
Craig and Sophie share 60 chocolates.
They divide them in the ratio 2 : 3 with Sophie having the larger share.
How many chocolates does Sophie have?
...............................................................................................................................................
...............................................................................................................................................
Answer .........................................................................
(Total 2 marks)
7.
Two friends agree to share £42 in the ratio 3 : 4
How much is the smaller share?
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer £ .............................................................
(Total 2 marks)
The Robert Smyth School
3
The Robert Smyth School
Mathematics Faculty
Topic 6
Ratio HW 2
Innovation & excellence
Answers - Topic 6 (Foundation) – Homework on Using Ratio
1.
(a)
16 : 24
M1
or 24 : 16 or 3 : 2
2:3
A1
or 1 : 1.5
8
40
(b)
M1
or
2.
1
or 0.2
5
(their 0.2) × 100
M1
20
A1
4 parts
 Alice receives
3
× 12
4
=9
M1
A1
M1 for 3:9
[2]
3.
Number of chocolate is
4
× 40
5
= 32
M1
A1
SC1 8 or 8 and 32
[2]
4.
Total number of songs is 5
 Dan receives 15 × £80
M1
= £16
A1
[2]
5.
(a)
(i)
(ii)
(b)
4 + 1 = 5, 40  5 (=8)
M1
8
A1
24
B1
Percentage =
= 60
24
× 100
40
M1
A1
[5]
The Robert Smyth School
4
The Robert Smyth School
Mathematics Faculty
Topic 6
Ratio HW 2
Innovation & excellence
6.
Number of chocolates is
3
× 60
5
= 36
M1
A1
SC1 24 or 24 and 36
[2]
7.
3:4  7 parts
Smaller is
3
× 42
7
M1
= 18
A1
SC1 24
[2]
The Robert Smyth School
5